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Class 4Fractions
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Answer the questions
(1) Solve : 1
22 +
2
22 +
3
22
(2) Shade the images to show the following fraction subtraction.
9
10 −
4
10 =
− =
(3) What is the value of ?
4
17 +
17 +
1
17 +
6
17 = 1
(4) George read 7
8 of a book in two days. If George read
4
8 of the book on the first day. What fraction
of the book he read on the second day?
(5) The following figure shows different fruits in a basket. What fraction of the fruits are pomegranates?
(6) The perimeter of a square board is 5
7 m. Find the length of each side in meters.
(7) What fraction is represented by shaded portion of these shapes :
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A)
B)
C)
D)
E)
F)
(8) What will be the numerator of the fraction representing the unshaded part in the given figure ?
(9) Tina's school is 6
7 kilometers away. She normally picks up her friend on her way to school. If the
distance of her friend's house is 5
7 kilometers from her house. Find the distance of the school from
her friend's house?
(10) Write the mixed fraction representred by the figure given below.
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Choose correct answer(s) from the given choices
(11) The figure representing the fraction of the shaded part equivalent to 8
14 is ______.
a. b.
c. d.
Fill in the blanks
(12) Add the following fractions:
A) 3
10 +
5
10 =
B) 3
12 +
8
12 =
C) 1
3 +
1
3 =
D) 7
17 +
7
17 =
E) 3
15 +
8
15 =
F) 5
16 +
6
16 =
(13) Add the following fractions and reduce them to the simplest form:
A) 5
4 +
8
2 = B)
5
9 +
4
5 = C)
3
8 +
7
2 =
D) 4
5 +
7
10 = E)
1
5 +
8
7 = F)
5
3 +
6
2 =
(14) A fraction in which the denominator is smaller than the numerator is called an
fraction.
(15) In like fractions, the numerator, the smaller the fraction will be.
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Answers
(1) 6
22
Step 1
1
22 ,
2
22 and
3
22 are ‘Like Fractions’ - that is, their denominators are the same.
Step 2
In order to add three Like Fractions, we need to add the numerators together and the denominatorremains the same.
Step 3
So, 1
22 +
2
22 +
3
22 =
6
22
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(2) 9
10 −
4
10 =
5
10
− =
Step 1
A proper fraction represents a part of a whole. In the given figures, each circle represents onewhole thing, and has been divided into 10 equal parts.
Step 2
The fact that only 9 parts are shaded in the first circle tells us that it represents the fraction 9
10
or ‘9 parts of a thing that has been broken into 10 parts’.
Step 3
Similarly, the second circle represents ‘4 parts of a thing that has been broken into 10 parts’.
Step 4
9 parts minus 4 parts of something that has been broken into 10 parts will be same as ‘5 parts out
of 10’, or 5
10 .
Step 5
So, our answer is 5
10 and this can be represented using the third circle by shading 5 parts out of
10.
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(3) 6
Step 1
It is given that sum of fractions is equal to 1. Therefore, numerator and denominator of the sumshould be equal.
Step 2
On addition of fraction we get:
4
17 +
17 +
1
17 +
6
17 =
4 + + 1 + 6
17
Step 3
As we know that numerator and denominator of sum are equal:4 + + 1 + 6 = 17
Step 4
Now, we can be seen that the above relation is satisfied only when is equal to 6.
Therefore, = 6
(4) 3
8
Step 1
Fraction of the book read by George in two days = 7
8
Fraction of the book read by George on the first day = 4
8
Step 2
Fraction of the book read by George on the second day = Fraction of the book read by George intwo days − Fraction of the book read by George on the first day
= 7
8 −
4
8
= 7 − 4
8
= 3
8
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(5) 5
15
Step 1
Let us count all fruits in the given box. There are total 15 fruits, out of which 5 are pomegranates.
Step 2
Therefore, fraction of pomegranates = Number of pomegranates
Total number of fruits
= 5
15
(6) 5
28 m
Step 1
According to the question, the perimeter of the square board is 5
7 m and we have to calculate
the length of each side.
Step 2
We know that the perimeter of a square = 4 × side of the squareSo, to calculate the side of the given square, we have to divide the perimeter by 4.Side of the square = Perimeter of the square ÷ 4
= 5
7 ÷ 4
= 5
7 ×
1
4 =
5
28
Step 3
To convert the fraction into the simplest form, let us divide the numerator and denominator of theabove fraction by their H.C.F, that is 1.
5
28 =
5
1
28
1
= 5
28
Step 4
Hence, the length of each side of the square board is 5
28 m.
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(7) A) 9
10
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 10Number of parts that are shaded in the image = 9
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 9
10
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 9
10 .
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B) 7
9
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 9Number of parts that are shaded in the image = 7
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 7
9
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 7
9 .
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C) 5
10
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 10Number of parts that are shaded in the image = 5
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 5
10
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 5
10 .
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D) 4
8
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 8Number of parts that are shaded in the image = 4
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 4
8
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 4
8 .
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E) 2
4
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 4Number of parts that are shaded in the image = 2
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 2
4
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 2
4 .
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F) 7
8
Step 1
We have been asked to find the fraction that represents the shaded portion of thefollowing shape:
Step 2
Total number of equal parts in the image = 8Number of parts that are shaded in the image = 7
Step 3
Fraction of parts of the image that are shaded = Number of shaded parts
Total number of parts
= 7
8
Step 4
Hence, the fraction that is represented by the shaded portion of the shape is 7
8 .
(8) 5
Step 1
We know that a fraction means a part of the whole where the numerator of the fraction representsthe number of parts we have and the denominator represents the total number of parts the figure isdivided into.
Step 2
In the given figure, 5 out of 13 parts are unshaded.Therefore, the numerator of the fraction representing the unshaded part is 5.
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(9) 1
7
Tina picks up her friend on her way to school. This means that her friend's house is located on herway to school.So, Distance between the school and her friend's house = Distance between her house and theschool − Distance between her house and her friend's house
= 6
7 −
5
7
= 6 − 5
7
= 1
7
(10) 55
9
Step 1
A mixed fraction has two parts:
1. A whole number representing few whole/complete entities.2. a proper fraction representing a specific part of a whole entity.
Step 2
Here, we can see that there are 5 figures that are shaded completely. They represent the wholenumber part 5 of the mixed fraction.
Step 3
The last figure has 5 out of 9 parts shaded. This represents the proper fraction part 5
9 of the
mixed fraction.
Step 4
Hence, the mixed-fraction shown by the given figure is 5 + 5
9 , or 5
5
9 .
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(11) a.
Step 1
We know,
Fraction of the shaded part = Number of shaded parts
Total number of parts
Step 2
Let us find the fraction of the shaded part for each of the given options.
Option a: Fraction of the shaded part = 8
14
Option b: Fraction of the shaded part = 3
14
Option c: Fraction of the shaded part = 4
10
Option d: Fraction of the shaded part = 1
10
Step 3
We have to find the fraction that is equivalent to 8
14 .
Step 4
We find that 8
14 is the fraction of the shaded part of the figure given in option a. Hence, option a
is the correct answer.
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(12) A) 3
10 +
5
10 =
8
10
Step 1
3
10 and
5
10 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
10 +
5
10 =
8
10
B) 3
12 +
8
12 =
11
12
Step 1
3
12 and
8
12 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
12 +
8
12 =
11
12
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C) 1
3 +
1
3 =
2
3
Step 1
1
3 and
1
3 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 1
3 +
1
3 =
2
3
D) 7
17 +
7
17 =
14
17
Step 1
7
17 and
7
17 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 7
17 +
7
17 =
14
17
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E) 3
15 +
8
15 =
11
15
Step 1
3
15 and
8
15 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 3
15 +
8
15 =
11
15
F) 5
16 +
6
16 =
11
16
Step 1
5
16 and
6
16 are ‘Like Fractions‘, i.e. their denominators are same.
Step 2
In order to add two like fractions, we need to add the numerators together and keepthe denominator same.
Step 3
So, 5
16 +
6
16 =
11
16
(13) A) 5
4 +
8
2 =
21
4
Step 1
The fractions 5
4 and
8
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
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Let us first find the LCM of the denominators 2 and 4. The LCM is 4.
Step 3
To write 5
4 as an equivalent fraction which has 4 as denominator, we need to
multiply both the numerator and denominator by 4
4 = 1. So, the equivalent fraction is:
5 × 1
4 × 1 =
5
4
Step 4
Similarly, to write 8
2 as an equivalent fraction which has 4 as denominator, we need
to multiply both the numerator and denominator by 4
2 = 2. So, the equivalent fraction
is:
8 × 2
2 × 2 =
16
4
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
5
4 +
16
4 =
5 + 16
4 =
21
4
Step 6
In order to convert the fraction 21
4 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 21 and 4 is 1.
Step 8
Hence, the simplest/lowest form of 21
4 is
21
1
4
1
= 21
4
B) 5
9 +
4
5 =
61
45
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Step 1
The fractions 5
9 and
4
5 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 5 and 9. The LCM is 45.
Step 3
To write 5
9 as an equivalent fraction which has 45 as denominator, we need to
multiply both the numerator and denominator by 45
9 = 5. So, the equivalent fraction
is:
5 × 5
9 × 5 =
25
45
Step 4
Similarly, to write 4
5 as an equivalent fraction which has 45 as denominator, we need
to multiply both the numerator and denominator by 45
5 = 9. So, the equivalent
fraction is:
4 × 9
5 × 9 =
36
45
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
25
45 +
36
45 =
25 + 36
45 =
61
45
Step 6
In order to convert the fraction 61
45 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 61 and 45 is 1.
Step 8
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Hence, the simplest/lowest form of 61
45 is
61
1
45
1
= 61
45
C) 3
8 +
7
2 =
31
8
Step 1
The fractions 3
8 and
7
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 2 and 8. The LCM is 8.
Step 3
To write 3
8 as an equivalent fraction which has 8 as denominator, we need to
multiply both the numerator and denominator by 8
8 = 1. So, the equivalent fraction is:
3 × 1
8 × 1 =
3
8
Step 4
Similarly, to write 7
2 as an equivalent fraction which has 8 as denominator, we need
to multiply both the numerator and denominator by 8
2 = 4. So, the equivalent fraction
is:
7 × 4
2 × 4 =
28
8
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
3
8 +
28
8 =
3 + 28
8 =
31
8
Step 6
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In order to convert the fraction 31
8 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 31 and 8 is 1.
Step 8
Hence, the simplest/lowest form of 31
8 is
31
1
8
1
= 31
8
D) 4
5 +
7
10 =
3
2
Step 1
The fractions 4
5 and
7
10 are unlike fractions as their denominators are different.
We will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 10 and 5. The LCM is 10.
Step 3
To write 4
5 as an equivalent fraction which has 10 as denominator, we need to
multiply both the numerator and denominator by 10
5 = 2. So, the equivalent fraction
is:
4 × 2
5 × 2 =
8
10
Step 4
Similarly, to write 7
10 as an equivalent fraction which has 10 as denominator, we
need to multiply both the numerator and denominator by 10
10 = 1. So, the equivalent
fraction is:
7 × 1
10 × 1 =
7
10
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Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
8
10 +
7
10 =
8 + 7
10 =
15
10
Step 6
In order to convert the fraction 15
10 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 15 and 10 is 5.
Step 8
Hence, the simplest/lowest form of 15
10 is
15
5
10
5
= 3
2
E) 1
5 +
8
7 =
47
35
Step 1
The fractions 1
5 and
8
7 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 7 and 5. The LCM is 35.
Step 3
To write 1
5 as an equivalent fraction which has 35 as denominator, we need to
multiply both the numerator and denominator by 35
5 = 7. So, the equivalent fraction
is:
1 × 7
5 × 7 =
7
35
Step 4
Similarly, to write 8
7 as an equivalent fraction which has 35 as denominator, we need
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to multiply both the numerator and denominator by 35
7 = 5. So, the equivalent
fraction is:
8 × 5
7 × 5 =
40
35
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
7
35 +
40
35 =
7 + 40
35 =
47
35
Step 6
In order to convert the fraction 47
35 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 47 and 35 is 1.
Step 8
Hence, the simplest/lowest form of 47
35 is
47
1
35
1
= 47
35
F) 5
3 +
6
2 =
14
3
Step 1
The fractions 5
3 and
6
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 2 and 3. The LCM is 6.
Step 3
To write 5
3 as an equivalent fraction which has 6 as denominator, we need to
multiply both the numerator and denominator by 6
3 = 2. So, the equivalent fraction is:
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5 × 2
3 × 2 =
10
6
Step 4
Similarly, to write 6
2 as an equivalent fraction which has 6 as denominator, we need
to multiply both the numerator and denominator by 6
2 = 3. So, the equivalent fraction
is:
6 × 3
2 × 3 =
18
6
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
10
6 +
18
6 =
10 + 18
6 =
28
6
Step 6
In order to convert the fraction 28
6 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 28 and 6 is 2.
Step 8
Hence, the simplest/lowest form of 28
6 is
28
2
6
2
= 14
3
(14) improper
A fraction in which the denominator is smaller than the numerator is called an improper fraction.
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(15) smaller
Step 1
Like fractions are those who have the same denominator. For such fractions the value of theoverall fraction depends directly on the value of their numerator.
Step 2
Therefore, in like fractions, smaller the numerator, smaller is the fraction.
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